sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([33,11,21]))
pari:[g,chi] = znchar(Mod(17,966))
χ966(5,⋅)
χ966(17,⋅)
χ966(89,⋅)
χ966(143,⋅)
χ966(227,⋅)
χ966(341,⋅)
χ966(383,⋅)
χ966(425,⋅)
χ966(467,⋅)
χ966(479,⋅)
χ966(521,⋅)
χ966(563,⋅)
χ966(605,⋅)
χ966(635,⋅)
χ966(677,⋅)
χ966(773,⋅)
χ966(803,⋅)
χ966(815,⋅)
χ966(845,⋅)
χ966(941,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(323,829,925) → (−1,e(61),e(227))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 25 | 29 | 31 | 37 | 41 |
χ966(17,a) |
−1 | 1 | e(6643) | e(331) | e(2221) | e(6659) | e(3320) | e(3310) | e(225) | e(665) | e(661) | e(119) |
sage:chi.jacobi_sum(n)
sage:chi.gauss_sum(a)
pari:znchargauss(g,chi,a)
sage:chi.jacobi_sum(n)
sage:chi.kloosterman_sum(a,b)